Quadratic Ideals, Indefinite Quadratic Forms and Some Specific Diophantine Equations
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, vol.36, no.3, pp.173-192, 2018 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 36 Issue: 3
- Publication Date: 2018
- Doi Number: 10.5269/bspm.v36i3.30799
- Journal Name: BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.173-192
- Bursa Uludag University Affiliated: Yes
Abstract
Let k >= 1 be an integer and let P = k + 2, Q = k and D = k(2) + 4. In this paper, we derived some algebraic properties of quadratic ideals I-gamma and indefinite quadratic forms F-gamma for quadratic irrationals gamma, and then we determine the set of all integer solutions of the Diophantine equation F-gamma(+/- k) (x, y) = +/- Q.